A304237 - OEIS

%I #20 Jun 28 2018 14:59:34

%S 10,101,11,110,201,12,21,102,121,111,112,210,202,22,122,211,120,301,

%T 13,31,103,131,113,231,123,310,203,32,23,132,212,220,302,213,232,221,

%U 124,41,14,141,114,241,125,51,15,151,115,251,126,61,16,161,116,261,127,71,17,171,117,271,128,81,18,181,118

%N a(n) is the smallest positive integer not yet in the sequence that is obtained when the first and last digits of a(n-1) are exchanged and used in a(n) in the exchanged order (but not necessarily adjacent); a(1)=10.

%C Up to n=82, the only consecutive numbers in the sequence are 111, 112 and 222, 223.

%C Could have started sequence with offset a(0)=0 and it would be the same sequence.

%e a(2)=101 since 101 is the smallest positive number not yet in the sequence that is obtained when the first and last digits of a(1)=10 are exchanged and used in that order.

%e a(8)=102 since 102 is the smallest positive number not yet in the sequence that is obtained when the first and last digits of a(7)=21 are exchanged and used in that order (but not necessarily adjacent).

%o (PARI) firstTerms(n)={my(Seq=vector(n),a=[1,0],c,y,k,h=Vecsmall(0,1000*n));print1("10,");Seq[1]=10;h[11]=1;for(i=2,n,for(t=11,oo,if(!h[t+1],c=digits(t);y=1;while((y<#c)&&(!c[y]),y++);forvec(u=[[y,#c],[y,#c]],if(k=([c[u[1]],c[u[2]]]==[a[#a],a[1]]),break),2);if(k,Seq[i]=t;print1(t",");a=c;h[t+1]=1;break))));return(Seq)} \\ _R. J. Cano_, May 11 2018

%Y Cf. A107353, A303605.

%K nonn,base

%O 1,1

%A _Enrique Navarrete_, May 08 2018